The recognition of comorbidities is relevant for asthma management, especially if these conditions/diseases are treatable traits such as anxiety. This study aimed to explore the associations between asthma severity and child and parent asthma-related anxiety and to recognize the most common specific fears. This cross-sectional study consisted of 150 parents and their children diagnosed with asthma, and was conducted at the Pediatric Clinic of the University Hospital Center Split in Croatia. All children, from ages 3 to 17 years, underwent a thorough clinical examination. A total of 150 parents and 108 children filled out an asthma-related anxiety questionnaire in paper form. Parents of children with moderate and severe asthma had higher asthma-related anxiety due to restrictions related to asthma symptoms (p = 0.032), and children diagnosed with moderate and severe asthma had greater anxiety due to restrictions related to asthma symptoms than children diagnosed with mild asthma (p = 0.004). Children's anxiety was the highest when they experienced an asthmatic attack during physical activity (PA), and they fear that they will not be successful in sports or dancing due to asthma. Parents commonly reported the fear of an asthma attack without warning signs (p < 0.001), fear of drug side effects (p < 0.001), fear of absence from school (p = 0.006), and fear of an asthma attack during PA (p < 0.001). The current study reports findings of increased parental levels of anxiety when compared to their children, related to fear of an asthma attack occurring without warning signs, fear of side effects and fear of absence from school, as well as the fear of an asthma attack occurring during sports activities. When assessing individual items on anxiety associated with asthma, children most commonly reported concern related to physical activity.